Theorems · Theorem · number theory
Int.fib_succ_mul_fib_pred_sub_fib_sq
∀ (n : ℤ), Int.fib (n + 1) * Int.fib (n - 1) - Int.fib n ^ 2 = (-1) ^ n.natAbs
Cassini's identity: fib (n + 1) * fib (n - 1) - fib n ^ 2 = (-1) ^ |n|.
- Defined in
- Mathlib.Data.Int.Fib.Lemmas
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
- Nat.cast_zeroproof · cited by 1,870
- pow_zeroproof · cited by 1,094
- sub_eq_add_negproof · cited by 1,023
- sub_zeroproof · cited by 938
- Nat.cast_addproof · cited by 586
- neg_zeroproof · cited by 542
- Evenproof · cited by 444
- zero_powproof · cited by 361
- zero_subproof · cited by 335
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.